Problem solving

Question

Teacher gave candies to his class. He gave each boy as many candies as there were boys in the class. Likewise to girls. He had bought 400 candies. When he finished giving them out he had 6 left. How many students were in his class?

Answer 1

B is the number of boys in the class

G is the number of girls in the class

B and G are positive integers

B^B + G^G + 6 = 400

B^B + G^G = 394

Are there positive integers B and G that

solves that equation?

Note that 5^5 = 3025 which is way too big

I don't think so